A mystery that’s endured throughout the Rolling Stones’ 50 years of music and mayhem has been exactly who decided it was the greatest rock ’n’ roll band in the world.

“Crossfire Hurricane,” the breezy new nearly 2-hour documentary celebrating the British bad boys’ golden anniversary gives us at least one answer. It’s the fans, the film claims, as one young man voices that sentiment during a mid-’60s news clip amidst footage of frenzy and chaos at the Stones’ live shows — band bassist Bill Wyman recalling the “flood of urine” he would watch stream down the aisles from excited girls.

Wyman may (we hope) be overstating the case, but “Crossfire Hurricane” — which debuted at the London Film Festival in October and premieres Nov. 15 on HBO — certainly conveys the fury of the, well, storm that surrounded the Stones during their heyday and the mania attendant throughout the band’s long run. There are no bombshells or revelations here; instead director Brett Morgen favors a brisk telling of the legend through key events and crucial songs. “Crossfire Hurricane” certainly makes the point that it’s been more than only rock ’n’ roll, but at the same time it lets us know that a mostly good time has been had by all.

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The present-day Stones, both current and former members, are decidedly part of the film, but through voiceovers and never seen on camera — a storytelling technique Morgen copped from his 2002 adaptation of film producer Robert Evans’ “The Kids Stays in the Picture.” It’s a bit odd at first, but it also gives “Crossfire Hurricane” a bit of scholarly gravitas; instead of the chiseled and aged Stones being the stars of the show, it’s their past that shines, with the contemporary commentary from the disembodied voices providing context.

As Mick Jagger notes at the end of the film, “you can’t be young forever,” but by not seeing him or any of the others, “Crossfire Hurricane” preserves the Stones at their most potent and virile.

The footage hails from a variety of familiar sources, including “The Dick Cavett Show,” Peter Whitehead’s recently released “Charlie is My Darling — Ireland 1965,” the Mayles brothers’ definitive “Gimme Shelter” and Robert Frank’s lurid and (officially) unreleased “C***sucker Blues.” We see the Stones cavorting backstage, in the studio, in hotel rooms and in tour vehicles; an impossibly young-looking Jagger moons the camera and also snorts cocaine from the blade of a switchblade knife. Guitarist Keith Richards recalls that in the early days, “we didn’t play a show that ever was completed, for two or three years” because of fans storming the stage and riots in the seats.

The group also addresses its prescribed role — the grand plan of original manager Andrew Loog Oldham — to make the Stones the antithesis of their more polished rivals, the Beatles. “The Beatles got the white hat,” Richards explains. “What’s left? The black hat.”

“Crossfire Hurricane” parses its running time judiciously and hones in on:

The 1967 drug bust at Richards’ Redlands home that briefly landed him and Jagger in jail.

Sex and drugs in general.

The 1969 Altamont Speedway concert where a fan was killed.

Mick Taylor’s departure from the band in 1974, with Ron Wood of the Faces taking his place.

Richards’ 1977 drug bust in Toronto.

There’s also a nice collage of images and discussion about Jagger’s and Richards’ evolution into songwriters while “(I Can’t Get No) Satisfaction” plays.

And rather than trying to cram in as many songs as he can, Morgen treats us to long and incendiary live renditions of anthems such as “Street Fighting Man,” “It’s All Over Now,” “Sympathy For the Devil” (from the “The Rolling Stones Rock and Roll Circus”), “Midnight Rambler” and the 1976 album track “Hey Negrita.”

But “Crossfire Hurricane” hardly tells the whole tale. The narrative largely stops at about 1978, with the last 3-plus decades blown through in mere minutes, skipping the mid-’80s schism that nearly ended the band, and Wyman’s departure in 1993.

There’s certainly more to the story than any director could handle in just two hours, but the film leaves us with the impression that the Stones’ vaunted history has been 20 or so glorious years that mattered and another 30 that just happened — a glaring shortcoming in an otherwise engaging peek at the eye of the “Hurricane.”

GOT STONES IF YOU WANT IT

The Rolling Stones’ 50th anniversary has not only brought the iconic rock group back on the road — for concerts Nov. 25 and 29 in London, Dec. 13 and 15 in Newark, N.J., and more dates planned for 2013 — but has also delivered a new batch of Stones-related products for those seeking a little more, er, satisfaction. Here’s what’s out there:

“GRRR!” (UMe): Due out Nov. 13, the Stones’ latest best-of set featuring a pair of new songs — “Gloom and Doom” and “One Last Shot” — recorded earlier this year in Paris with Detroit-born producer Don Was. “GRRR!” comes in four configurations including three- and four-CD versions, a four-CD Super Deluxe Edition and a vinyl box set.

“Charlie is My Darling — Ireland 1965” (ABKCO): This long-lost documentary about one of the group’s early tours of the Emerald Isle surfaced this year, offering an intimate look at the Stones at a somewhat more innocent point of their career. A Super Deluxe Box Set edition of the film includes a soundtrack as well as a live album from England the same year. “Charlie is My Darling” has also just started showing on DirectTV’s Audience Network.

“The Rolling Stones 50” (Hyperion Books): This lavish, officially authorized coffee table book is the official “program” of the Stones’ 50th anniversary, with 352 pages of photos both rare and familiar and commentary by the band members. A hefty tome with a hefty ($60) price tag to go with it.

“Muddy Waters/The Rolling Stones/Checkerboard Lounge/Live Chicago 1981” (Eagle Vision): While hanging out in Chicago between shows on their 1981 tour, the Stones stopped to pay homage to one of their influences and mentors — and the guy who inspired the group’s name. The Stones are appropriately solicitous of Waters, then 68, but that doesn’t mean tame. And raw renditions of “Mannish Boy,” “Hoochie Coochie Man,” “Champagne and Reefer” and other classics are nothing less than historic.

“Mick Jagger” by Philip Norman (Ecco): Jagger isn’t the only Stone that matters, of course, but he’s certainly the most gossiped about, and his knack for discretion makes him that much juicier of a subject. British author Norman has previously written about the Stones as well as the Beatles, John Lennon and Elton John, and if these 622 pages don’t necessarily open Jagger up as never before, it at least paints a complete and professionally balanced compendium